Helmholtz resonators represent one of the most utilized acoustic objects whose popularity was re-gained with the rise of metameterials. Despite the long history of investigations, the description still can be regarded as incomplete, and one of the gaps lies in the area of acousto-mechanical coupling. We contribute to solving the problem by providing a wide-range parametric analysis of Helmholtz resonators prepared as cylinders with longitudinal slits (parallel to the cylinder axis). Resonance frequencies of such resonators are evaluated depending on geometric parameters of the cylinders (slit width and wall thickness) as well as mechanical characteristics of the material making the resonators. In particular, we reveal an interplay between acoustic resonances and vibrational resonances of the walls, which may be qualitatively different depending on the parameters and materials. Given the absence of reliable analytical models (except for idealised limiting cases), we deem our results useful for any practical implementation of such resonators, especially for the design of acoustic metastructures.
Pavliuk et al. (Thu,) studied this question.